DRAM circuits (sometimes called DRAM's or DRAM devices) are used in computers and other electronic devices to store information. To keep the information intact, a DRAM circuit is periodically refreshed even if there is no read/write access to the circuit from other circuits. Refresh can be accomplished either by externally initiated refresh operations (i.e., under the control of commands sent by a device or circuit external to the DRAM) or by self-refresh, in which refresh operations are timed and controlled by circuitry internal to the DRAM. Refreshing the memory cells of a DRAM typically requires two operations: first reading the data in multiple memory cells (e.g., a row) and then writing the data back into the memory cells. The refresh operation consumes energy because it requires charging and discharging capacitors in the memory cells. In the course of refreshing a memory cell, it is also necessary to charge and discharge the capacitance of the bit line and word line structures that are coupled to the cell. Although refreshing a single row of memory cells uses very little energy, the DRAM circuit may expend a significant amount of energy on refresh operations because it has many rows of memory cells and needs to refresh them quickly and repeatedly. The energy used by refresh operations is ultimately turned into heat, which may cause or contribute to thermal issues in an electronic application that includes the DRAM circuit. For example, the application may need to incorporate an additional heat dissipation device in order to dissipate the heat generated by the DRAM circuits in the application, thereby increasing both the application's cost and size. Also, in a portable application, the energy used for refresh operations represents a continuous battery drain, and reducing the energy cost of refresh will increase the time interval until the battery needs recharging.